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Full text of "Analytical Mechanics"

CENTER OF MASS AND MOMENT OF INERTIA     161
Denoting the moment of inertia of the circular lamina by Ii and that •of the rectangular lamina by I2 we have
2  2
:+/v
ma
2
/a2 .   Z2\
-Ki + w
which is identical with the result obtained by the direct method.
PROBLEMS.
1.   Find the moment of inertia of a hollow circular cylinder with re-.spect to, (a) its geometrical axis, (b) an element, (c) a transverse axis through the center of mass.
2.   Find the moment of inertia of an elliptical cylinder with respect to, (a) its geometrical axis, (b) a transverse axis through its center of mass and parallel to the major axis of a right section.
3.   Find the moment of inertia of a rectangular prism with respect to, (a) its geometrical axis, (b) a transverse axis through the center of mass and perpendicular to one of its faces.
4.   In the preceding problem suppose the prism to be hollow.
6. Find the moment of inertia of a prism, the cross section of which is .an equilateral triangle,, with respect to, (a) its geometrical axis, (b) a transverse axis through its center of mass and perpendicular to one of its faces.
6.   In the preceding problem suppose the prism to be hollow.
7.   Find the moment of inertia of a hollow sphere with respect to, (a) -a diameter, (b) a tangent line.
8.   Find the moment of inertia of a spherical shell of negligible thickness with respect to a tangent line.
9.   Find the moment of inertia of a right circular cone with respect to, •(a) its geometrical axis, (b) a transverse axis through the vertex.
10.   In the preceding problem suppose the cone to be a shell of negligible thickness.
11.   Find the moment of inertia of a paraboloid of revolution with respect to, (a) its axis, (b) a transverse axis through its vertex.   The radius of the base is a and the height is h.